Uses of the Saphea Arzachelis
There are a number of things the Saphea can do that you can’t do on a Planispheric astrolabe, and vice versa. We will look at some of these here.
1: To find the Sun’s right ascension and declination on any date
First, find the Sun’s Zodiac position from the calendar rings. If today is the 12th July, then we are at Cancer 20.
Find the Cancer 20 point on the Ecliptic line, and you’ll see it is at 22º declination. The polar arcs show it at 68º Right Ascension, or 4.5 hours from the meridian.
2: Finding the times of Sunrise and Sunset for any date, for any latitude
First, find the Sun’s zodiac position again. Let’s continue with July 12, so we know it’s Cancer 20 today.
Move the Ruler so that the required latitude is read from the top left quadrant. I’m writing this in Central Texas, so I’ll use my location of 30º latitude.
Look at which declination arc crosses the Zodiac at Cancer 20. This shows 22º of declination (red line). The point where it meets the regula (the local horizon) is the time of sunrise. In this case it is 5:05 AM (remember, each polar arc represents 20 minutes).
Follow the same polar arc straight down to the lower set of numbers, and this gives you sunset – here it is 6:55 PM.
The length of the red line is also the length of the day; the Sun will move from the regula’s horizon to the right hand edge (at noon) and back as the day goes on. You can therefore calculate the Sun’s altitude for different times of day (see next section).
Remember that all times are going to be in local solar time and will need corrections for time zone location, daylight savings etc. (This is described in my Planispheric Astrolabe manual).
3: Finding the Sun’s altitude for a given day and time
Continuing with our July 12 example, what will the Sun’s altitude be at 10AM? (Or 2PM, if you use the lower set of numbers).
Use the Brachiolus pointer to mark the position where the 10am polar arc crosses the declination arc (currently 22º).
Then, rotate the ruler and brachiolus together, so that the ruler lies horizontally on the equinoctial line. The brachiolus is now pointing to the parallel marking the Sun’s altitude.
4: Find the maximum altitude of the sun for any latitude, given the sun’s declination.
In example 1, we found the Sun’s declination for July 12, which was 22º.
Put the ruler horizontally on the equinoctial line, and extend the Brachiolus to the edge of the dial. Mark the 22º position.
Turn the ruler so that it meets the position equalling 90º-(latitude); in this case 90-30=60, so move the ruler/pointer combination to the 60º mark. The pointer now reads 82º.
So to find the maximum altitude for the Sun on any day, at any latitude, you first work out the declination for the day (as above) and then the altitude.
(You can check this with a planispheric astrolabe if you have the plate for the same latitude, by moving the rete such that 90º is on the meridian.)
5: Converting between Right Ascension/Declination and Celestial Lat/Long
You always start with the regula aligned on the equinoctial line. In one coordinate system (Equatorial) this represents the horizon. In the other system (Ecliptic) the line represents the ecliptic. This is the base line of each system and is what you are converting from.
Position the tip of the brachiola to the point you wish to convert. Then move the regula/brachiola to the ecliptic line and read off the coordinates in the other system.
Take Sirius, whose Right Ascension is 6h45m (101.2º) and declination is -16h42m (-16.716º).
Move the brachiola to that location on the plate, while the regula lies horizontally on the equinoctial line. Then move both together so the regula is aligned with the ecliptic.
The astrolabe shows the celestial lat/long to be +08º and 101º.
6: Finding the current time from the altitude of the Sun or a star
This is actually not very easy to do on the Saphea and is one of the main reasons that a Planispheric astrolabe exists on the other side of the instrument. It is easy to do with that side, provided you have the correct latitude plate installed.
(If you own one of my standard Planispheric astrolabes, the plates are interchangeable with this device, so if you have extra plates you can use them here)
To do this on the Saphea, do the following:
- Take a sighting of the altitude of the Sun or bright star using the combined ruler/alidade on the other side of the instrument.
- Orient the regula to the polar distance for the latitude (90-latitude=polar distance)
- Move the brachiolus so that its point lies on the declination of the Sun/star and on an hour arc close to what you think the time is
- Rotate the regula to the equinoctial line and see where the tip of the brachiolus is.
- If the tip is on the parallel marked by the measured altitude, then you got the time guess right!
- If it’s not, then guess again; move the brachiolus to another time and repeat the last four steps.
